I read on this site possible methods to make my eBook permanently free on amazon but I'd like to know if I go this route and it is successful will I still be able to print copies of that title?
You can sell print on demand copies through Amazon's https://www.createspace.com/. When you finish setting up the title after entering page count, trim size, matte or gloss cover, etc. it will generate a 'minimum list price' typically around 5 dollars for the average paperback in my experience. This is how much it costs amazon to print it and also how low you can set the price of your paperback if you choose to distribute through amazon.
Also worth noting is the fact that your print copy book and ebook should have different ISBNs - there is a way to link them in helix if you would like - but the bottom line here is that how you distribute and sell your ebook and how you distribute and sell your print book do not directly impact one another.